Welcome to iMore! Is your iPhone itself connected to the Internet? Are other apps able access the internet? Are you on wifi or using a cellular data connection? Here's a few suggestions:

1. If you're on cellular go to Settings > Cellular, then scroll down your app list and make sure that Safari is toggled on. While you're on that screen, go to the top and make sure that Cellular Data is also toggled on and Enable LTE is set to either Data Only or Voice & Data.

2. Conduct a hard reset by holding down the power button and home button until you see the Apple boot logo.